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Published byPatricia Body Modified about 1 year ago

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Introduction to Structural Member Properties

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Structural Member Properties Moment of Inertia (I) is a mathematical property of a cross section (measured in inches 4 ) that gives important information about how that cross- sectional area is distributed about a centroidal axis. In general, a higher moment of inertia produces a greater resistance to deformation. Stiffness of an object related to its shape ©iStockphoto.com

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BeamMaterialLengthWidthHeightArea ADouglas Fir8 ft1 ½ in.5 ½ in.8 ¼ in. 2 BDouglas Fir8 ft5 ½ in.1 ½ in.8 ¼ in. 2 Moment of Inertia Principles Joist Plank

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Will beam A or beam B have a greater resistance to bending, resulting in the least amount of deformation, if an identical load is applied to both beams at the same location? What distinguishes beam A from beam B? Moment of Inertia Principles

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Calculating Moment of Inertia – Rectangles Why did beam B have greater deformation than beam A? Moment of Inertia Principles Difference in moment of inertia due to the orientation of the beam h

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Calculating Moment of Inertia Calculate beam A moment of inertia

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Calculating Moment of Inertia Calculate beam B moment of inertia

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Moment of Inertia 14Times Stiffer Beam A Beam B

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Moment of Inertia – Composite Shapes Why are composite shapes used in structural design?

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Non-Composite vs. Composite Beams Doing more with less Area = 8.00in. 2 Area = 2.70in. 2

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Modulus of Elasticity (E) The ratio of the increment of some specified form of stress to the increment of some specified form of strain. Also known as coefficient of elasticity, elasticity modulus, elastic modulus. This defines the stiffness of an object related to material chemical properties. In general, a higher modulus of elasticity produces a greater resistance to deformation. Structural Member Properties Chemical Makeup

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Modulus of Elasticity Principles BeamMaterialLengthWidthHeightAreaI ADouglas Fir8 ft1 ½ in.5 ½ in.8 ¼ in in. 4 BABS plastic8 ft1 ½ in.5 ½ in.8 ¼ in in. 4

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Modulus of Elasticity Principles What distinguishes beam A from beam B? Will beam A or beam B have a greater resistance to bending, resulting in the least amount of deformation, if an identical load is applied to both beams at the same location?

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Why did beam B have greater deformation than beam A? Modulus of Elasticity Principles Difference in material modulus of elasticity – The ability of a material to deform and return to its original shape Applied force or load Length of span between supports Modulus of elasticity Moment of inertia Characteristics of objects that affect deflection (Δ MAX )

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Calculating Beam Deflection BeamMaterialLength (L) Moment of Inertia (I) Modulus of Elasticity (E) Force (F) ADouglas Fir8.0 ft20.80 in. 4 1,800,000 psi 250 lbf BABS Plastic8.0 ft20.80 in ,000 psi 250 lbf

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Calculating Beam Deflection BeamMaterialLengthIELoad ADouglas Fir8.0 ft20.80 in. 4 1,800,000 psi 250 lbf Calculate beam deflection for beam A

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Calculating Beam Deflection BeamMaterialLengthIELoad BABS Plastic8.0 ft20.80 in ,000 psi 250 lbf Calculate beam deflection for beam B

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Douglas Fir vs. ABS Plastic 4.24 times less deflection

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